The current draw figures are probably steady-state - at turn on the motors might take more
than 100mA briefly. I'd add a 1N4148 across each motor as a free-wheel diode rather than
risk frying the TPIC6B595.
Alternatively use a 74HC595 driving a ULN2803, this can handle the current, has built in free-wheel
diodes, and will drop the voltage a bit (these motors are designed for 3.7V phone LiPo batteries, so
5V is pushing them rather hard).
You won't get single pin control from these shift registers, the best you can hope for is 2 pin
control (if you leave the latch pin in transparent mode). You can daisy chain '595 shift registers
so no limit to the number of motors if you have enough power and circuitboard/breadboard.
Use decoupling capacitors - if this means nothing, you need to do some simple research.